Quantifying harmonic hierarchies and key distances

In Carol L. Krumhansl, Cognitive Foundations of Musical Pitch. Oxford University Press USA (2001)
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Abstract

This chapter begins with two experiments that measure the relative structural significance of all possible major, minor, and diminished chords in major and minor key contexts. A well-defined harmonic hierarchy emerges that is considered in light of a number of possible influences, namely: tonal consonance; the statistical distribution of chords in tonal-harmonic music; and the positions of the component tones in the tonal hierarchy of the context key. The chapter concludes by deriving from the harmonic hierarchy a description of interkey distance, which can be compared to that derived from the tonal hierarchy.

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